Related papers: The Second Law of Quantum Complexity
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
In a recent paper Andrei N. Soklakov explained the foundations of the Lagrangian formulation of classical particle mechanics by means of Kolmogorov complexity. In the present paper we use some of Soklakov ideas in order to derive the second…
Given at PiTP 2018 summer program entitled "From Qubits to Spacetime." The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the…
It is established that black holes have entropy and behave as thermodynamical systems. Associating entropy to gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in…
We propose the use of a gravitational uncertainty principle for gravitation. We define the corresponding gravitational Planck's constant and the gravitational quantum of mass. We define entropy in terms of the quantum of gravity with the…
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
The Bekenstein-Hawking entropy satisfies the generalized second law of black hole thermodynamics for arbitrary thermodynamic evolution within Einstein-Maxwell theory. In contrast, the black hole entropy that satisfies the second law in…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of…
The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum…
A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy…
A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an…
The Second Law of Thermodynamics states that the entropy of a closed system is non-decreasing. Discussing the Second Law in the quantum world poses new challenges and provides new opportunities, involving fundamental…
The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian can be defined. The first law is established for stationary spacetimes, and the second law…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…